Amit Sehgal, Shubh N. Singh
Published 2019-01-24Version 1
The power graph of a given finite group is a simple undirected graph whose vertex set is the group itself, and there is an edge between any two distinct vertices if one is a power of the other. In this paper, we find a precise formula to count the degree of a vertex in the power graph of a finite abelian group of prime-power order. By using the degree formula, we give a new proof to show that the power graph of a cyclic group of prime-power order is complete. We finally determine the degree of a vertex in the power graph of a finite abelian group.
Degenerations and orbits in finite abelian groups
Cyclic-quasi-injective for Finite Abelian Groups
On the number of cyclic subgroups of a finite abelian group
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